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%I #31 Jun 05 2021 11:34:31
%S 1,2,4,5,6,10,12,17,22,45,87,217,546,17806,41850,127973,189586,435067,
%T 475810,595932,3319478,3737221,5741156,7349730,7473734,13114674,
%U 26076896,48515830,48791555,419983404,2217443166,2617207503,2894318150,8776851351,118596802796
%N Numbers k such that k divides 1 + Sum_{j=1..k} prime(j)^11.
%C a(47) > 3*10^13. - _Bruce Garner_, Jun 05 2021
%H Bruce Garner, <a href="/A233193/b233193.txt">Table of n, a(n) for n = 1..46</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e a(5)=6 because 1 plus the sum of the first 6 primes^11 is 2079498398712 which is divisible by 6.
%t p = 2; k = 0; s = 1; lst = {}; While[k < 41000000000, s = s + p^11; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)
%t With[{nn = 5*10^7},Select[Thread[{Accumulate[ Prime[ Range[nn]]^11] + 1, Range[nn]}], Divisible[#[[1]], #[[2]]] &][[All, 2]]] (* The program generates the first 29 terms of the sequence. To generate all 34, change the value of nn to 878*10^7, but the program will take a long time to run. *) (* _Harvey P. Dale_, Mar 09 2017 *)
%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K nonn
%O 1,2
%A _Robert Price_, Dec 05 2013
%E a(35) from _Karl-Heinz Hofmann_, Mar 07 2021
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